CBSE Class 12-science Answered

y = a sin (x + b) ….(1)

Differentiating both sides of equation (1) with respect to x,

y' = a cos (x + b) ...(2)

Differentiating equation (2) with respect to x,

y^'' = -a sin (x + b) ...(3)

From equations (1) and (2), we obtain,

y^'' + y = 0

This is the required differential equation.

OR

2xy dx + (x² + 2y²) dy = 0

Thus, the given differential equation is a homogeneous equation.

Substitute y = vx

Substituting the values of y and in equation (1), we obtain

Integrating both sides, we obtain